SOLUTION: A flagpole is secured on opposite sides by two guy wires, each of which is 7 ft longer than the pole. The distance between the points where the wires are fixed to the ground is equ

Question 156496: A flagpole is secured on opposite sides by two guy wires, each of which is 7 ft longer than the pole. The distance between the points where the wires are fixed to the ground is equal to the length of one guy wire. How tall is the flagpole? (to the nearest inch)
I have no idea how to solve this :(
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Think...right triangles!
The flag pole can be represented by the height of the right triangle, one of the guy wires can be represented by the hypotenuse of the right triangle, and the distance from the anchor point of one of the guy wires to the base of the flag pole can be represented by the base of the right triangle.
Now think about the Pythagorean theorem!
where c = the length of the hypotenuse (guy wire) = a+7, a = the height of the flag pole, and b = the length of the base (half of the length of one guy wire).
Let's see what all the measurements are:
c = the length of one guy wire = the height of the flag pole plus 7 ft.
a = the height of the flag pole and this is what we are trying to find.
b = half the length of one guy wire = (a+7)/2
So we'll make the appropriate substitutions into the formula and evaluate it.
Simplifying this, we get...
Subtract from both sides.
Multiply through by 4 to clear the fraction.
Subtract 56a from both sides.
Subtract 196 from both sides.
Use the quadratic formula to solve: Here, a = 1, b = -42, and c = -147. Change the variable from x to a.

or Discard the negative solution as the flag pole height is a positive value.
The flag pole is 45.25 feet or 543 inches.

RELATED QUESTIONS
A flagpole is secured on opposite sides by two guy wires, each of which is 5 ft. longer... (answered by Photonjohn)

A flagpole is secured on opposite sides by two guy wires, each of which is 6 ft longer... (answered by dabanfield)

A flagpole is supported by two guy wires on opposite sides. The wires are 35.3 feet and... (answered by josgarithmetic)

A vertical flag pole is 12 metres long. The flag pole is secured by several wires which... (answered by Alan3354)

A vertical flag pole is 12 metres long. The flag pole is secured by several wires which... (answered by rothauserc)

Two parallel guy wires are attached to a vertical pole 4.5m and 5.4m above the... (answered by stanbon)

a guy wire is a wire which is attached to an object and secured to the ground. quite... (answered by mananth,MathTherapy,greenestamps)

a 20 ft pole is supported by two wires that extend from the top of the pole to points... (answered by KMST)

a 30-foot pole is supported by two wires that extend from the top of the pole to points... (answered by nerdybill)